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Sunday, July 1, 2012

Unless you follow several mathematics education blogs or subscribe to certain Twitter feeds, you may well have missed the recent revival of the US Math Wars. The protagonists in the latest salvo are not the traditional foes, Mathematically Correct versus NCTM and MAA, but two groups who are making use of new technology in education, with Khan Academy squaring up against a number of web-savvy, younger mathematics and science educators who believe the US can and should do a lot better (and differently) in math ed than we do.I summarized some of my own views on KA in an article in The Huffington Post on March 20 of this year, but this article focuses on another issue than the one I discussed there. Namely, the large numbers of fanatical supporters Khan has gathered, who respond to even the mildest and well meaning criticisms of anything Khan with venom, hatred, and personal attacks.The first round of this new skirmish I was aware of (likely not the first to occur, since I check in only occasionally on developments in K-12 mathematics education, though now the excellent EdSurge provides me more useful news than I can possibly keep up with) was in February of this year when Mathalicious founder Karim Kai Ani posted a critique of KA pedagogy on his company blog. (Disclosure: I knew that posting was coming up, since Karim emailed me beforehand with questions about gamification and individually prescribed instruction, both of which he wanted to discuss in his article. I also voluntarily endorse his educational materials.)The KA–Mathalicious deluge began within a few hours of the blog being published, with a lot of the venom unleashed on Y-Combinator’s Hacker News. From the nature of many of the comments, which were personal, and often visceral attacks on Ani rather than reasoned responses to what was a very well thought out and cogently presented argument, it’s a reasonable assumption that they were contributed by schoolkids. Which to my mind makes this phenomenon worth thinking about. For schoolchildren are what K-12 education is about. When a substantial number of our main customers speak, we should listen, even if the method by which the message is delivered leaves a lot to be desired.Actually, I don’t know what percentage of the K-12 population is represented in those Hacker News (and other) blog posts, but what we do know is that Khan Academy has a large and devoted following. In some ways, I too am a fan of sorts, though less so than when I participated in a TV discussion with Sal back in 2010. For sure, I am dismayed by the huge number of mathematical errors and pedagogic shortcomings in his videos. (We’ve learned a lot about mathematics education in the past fifty years.) In the early days it was easy to overlook them – any new enterprise is buggy, particularly a one-person show like the early KA. But once the Silicon Valley millions started to roll in, and with those funds a staff, it would have been an easy Web exercise to crowdsource curriculum improvement/development to the many mathematics teachers and university mathematics education specialists who would surely have been eager to help.My enthusiasm came not from the KA site’s contents, but from something else I saw: Sal Khan himself. Up close – and I have met him a few times – he comes across as a really nice, approachable guy with a great sense of humor. Well, so do a lot of people. But there is something else. Sal has the ability to project that identity and that personality over the Web, using just his voice and the trace of a digital pen on a tablet. In the Age of Social Media, that, it seemed to me, was powerful. And, at least to date, extremely rare.Effective teaching is a human-to-human activity. Good teachers strive to achieve a connection with our students in the classroom. (I say “our students,” since I like to think I am a good teacher, albeit not at the K-12 level.) I’m told my voice conveys my enthusiasm for mathematics when I go on NPR as the Math Guy. If true, and some people seem to think so, then I can’t really take credit for it. I just speak into a microphone. No training, no rehearsing. Just me.Sal Khan has that natural ability in spades. As he tells us (all Silicon Valley enterprises have a creation story, and in his case it’s true), Khan Academy began as his attempt to help his younger cousins with their math homework, by posting video tutorials on YouTube. He did not set out to build an education empire. People outside his family simply came across his videos on the Web and found them useful.From a pedagogic perspective, his videos do not provide student learning, they deliver instruction – a distinction I discussed in my March Devlin’s Angle. It would be easy for me to critique them, and many have. (Read on.) But to me at least, providing learning is not where their real value lies. Learning mathematics is hard. Very hard. It is easy to get discouraged and give up. Some of us, when we are learning math the first time, are lucky enough to have a parent, grandparent, uncle or aunt, older sibling, or family friend who can sit down alongside us and help us. I suspect that a great many of today’s professional mathematicians owe their eventual success in the subject to someone who mentored them in the early days.But not everyone has such a person in their lives. At least, they did not until Sal Khan came along: friendly, non-threatening, patient, and a good explainer (actually not brilliant, but that might be all to the good, since a brilliant instructor could easily discourage a less-brilliant student). Above all, human. A regular guy. Just think about that for a moment. It’s a valuable weapon in the educational landscape.Much of the attraction of KA came from its very amateurish nature. It really was just Sal Khan in his converted closet. Sure he did not really understand (as a mathematician does) a lot of the math he explains (though he knows an awful lot more than most people), nor was he trained in mathematics pedagogy. (Ditto for me, BTW – on both counts! – though I think I know more about both than Sal, which makes it possible for me to critique many of his lessons.) But that was a huge part of what made KA so popular. Millions of people around the world, young and old, whose experiences of math class was or had been awful, saw him as on their side. He was everyone’s friendly, helpful Uncle Sal. (I hope this does not come across as a hagiography. I have a lot of issues with KA. But I am trying to understand what leads to KA having such a passionately supportive fan base. I think there is something for us all to learn here.)For millions of users of KA, what they find on the site is far better than anything they have had or are getting. For them, it’s not just a homework helper, it’s a lifeline. Their only lifeline.Sure, they probably don’t really learn any mathematics. (I have yet to be convinced you can really learn mathematics over the Web, though that does not stop me wanting to try, as indicated by my other blog MOOCtalk.) The fact is, many people actually don’t want to learn mathematics, they want to pass a math exam. And if Sal Khan helps them do that – and millions say that he has done exactly that – then is it surprising they become KA fans? (And educational establishment enemies!)Then Bill Gates comes along, and KA goes global. Expectations change. Now things have gotten more tricky. When a resource like KA becomes the primary vehicle by which millions of people acquire many or all of their mathematical skills, the stakes become dramatically higher than when it was a one-man homework-help service. Like it or not, ask for it or not, KA now has (in my view) an obligation to get things right. Doing so without destroying a major part of its appeal, is clearly going to be tricky.Which brings me to the more recent skirmishes.

On June 18, two math professors, John Golden and David Coffey, posted to YouTube a parody of Mystery Science Theater 3000, which they called MTT2K, in which they watched and critiqued a KA video (an old one, as it happens) about multiplying and dividing negative numbers. To my mind, the target of their theatrical sarcasm was not KA, rather the reverence that many seem to have for KA, but many Khan fans (perhaps the reverent ones) seem to have reacted differently.

In any event, KA immediately took down the video, replacing it with two new videos, one on Multiplying Positive and Negative Numbers, the other on Dividing Positive and Negative Numbers. The two new videos appear to have been made in direct response to the MTT2K critique. A short while later, Khan released another new video, Why a Negative Times a Negative is a Positive, providing further elaboration.Unfortunately, as John Jay High School (New York) physics teacher Frank Noschese noted, that third video was awfully similar to one produced some years earler by James Tanton. Things were escalating (or spiraling down, depending on your favored metaphor).The pity was that critiques by knowledgeable teachers and pedagogy experts resulting in modifications to KA instructional materials is surely the way to take something that has value and make it even more valuable. But that tended to get lost in the MTT2K-parody sarcasm and the barrage of name calling that followed.Incidentally, Noschese is a 2011 Presidential Award for Excellence in Math and Science Teaching awardee, and the author of an excellent science education blog Action-Reaction. He has commented and tweeted extensively (and to my mind constructively) on KA. I hope KA follows his blog and takes note of what he says.Another experienced STEM teacher with excellent suggestions (for KA and for teaching in general) is Dan Meyer, a former Google Education Fellow and now a PhD student in education at Stanford. He joined in the MTT2K exchange in his usually witty fashion in two blogposts, Bill Gates Just Put Out a Hit on John Golden and David Coffey, on June 20 and Sal Khan Comments On MTT2K In Chronicle of Higher Education, on June 28.The latter was about an article in the Chronicle of Higher Education that day, summarizing the MTT2K affair. The Chronicle article was inspired in part by the article by Justin Reich in Education Week on June 22 about the “MTT2K Prize”, a cash prize to be awarded for the best video commentary on a Khan Academy video. (Actually it’s a great idea, if it can be done collaboratively with KA, absent any negativity.)The final episode in this skirmish (at least so far, based on what I have seen) was an entry video to the MTT2K Prize competition on June 29, by Wired blogger Rhett Allain, an Associate Professor of Physics at Southeastern Louisiana University.To my mind, Allain’s blog description is better than his videoed critique. Allain just does not come across on video as well as Khan does. Many teachers, and most academics, spend a lot of their time critiquing one another. We get used to it. It’s how we learn and improve. But when you put it on YouTube, it is viewed by millions of people totally unfamiliar with the process, and they can – and, in the cases I am citing, did – react negatively.Which brings me back to my starting point. Education is hard, mathematics education particularly so. It takes a lot of different kinds of knowledge and expertise to get it right. The focal point is – and I think has to be – a single person, a teacher. Either in the flesh or over the Web. That teacher has to be able to connect to the students. Being a great classroom teacher does not make someone good at doing it on YouTube. In fact, most teachers come across pretty badly on video. But that does not matter if the people who are able to use the medium will listen to what they say.Sal Khan’s strength is that he comes across extremely well on video (with or without his face on screen!). I just wish he would work (with real experts) on the content more. But the real problem is not the stuff on the KA site. Flawed as it is, it is, as I noted earlier, a lot better than many people have, or ever had, access to. The fact that many of Khan’s fans describe him as “the best teacher ever” speaks volumes about the poor quality of the mathematics education that many receive. I’ve visited many math classrooms both in this country and around the world, and I’ve seen great math teaching. You won’t find it on KA. Instead, you will find something else, something unique and of value.Sure, KA has lots of weaknesses and could be improved. That goes for any product. The real problem is that the US (and other nations) identify mathematics learning with instruction and passing procedural tests. In that world, KA meets a clear market need for instruction to help people pass procedural math tests. In contrast, Ani, Noschese, Golden, Coffey, Meyer, Allain, and all the other KA critics in the educational world are interested in facilitating something quite different: real learning among their students.Sal Khan says he is trying to move into the real, conceptual learning space as well, but so far I have not seen much that would qualify, and as I noted earlier, my own interest in trying out the MOOC format notwithstanding, I have yet to be convinced that it is possible over the Web.Khan has something of real value to offer, most uniquely his ability to do well both locally and at a distance what many teachers find hard or impossible even in the classroom, namely connect with and inspire students. But he seems not to have deep conceptual understanding of mathematics or knowledge of the highly complex field of mathematics learning, and given his background it would be strange if he did. (For a good, reasoned series of articles pointing out the problems with KA, see the 2011 articles by Sylvia Martinez of Generation YES.)On the other side, there are many teachers and education researchers who do have knowledge of mathematics and mathematical pedagogy, but are not able to connect well, at least on video, where they come across as cold or impersonal or condescending – video is a harsh medium.If each party recognized that the others had something of value to offer, and if we could get beyond the squabbles and the name-calling, we could produce something that benefits the people we all care about: the students. Los Angeles police brutality victim Rodney King died recently. The words he famously uttered during the riots that followed his beating in 1992 seem equally pertinent to the current state of affairs regarding KA: “Can't we all get along?”

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The Mathematical Association of America is the world's largest community of mathematicians, students, and enthusiasts. We accelerate the understanding of our world through mathematics, because mathematics drives society and shapes our lives. Visit us at maa.org.